Fred Kline
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 Aug5 accepted Can we compile using only Integers Of Unusual Size? Aug5 comment Can we compile using only Integers Of Unusual Size? @kirma, make that an answer and I will accept it. Aug5 asked Can we compile using only Integers Of Unusual Size? Aug3 revised Collatz Tool Box — any speed ups possible? replaced uniqueRank to eliminate the Floor Aug3 revised Collatz Tool Box — any speed ups possible? removed || 0 == w from the Break[] which was a left-over from testing Aug2 revised Collatz Tool Box — any speed ups possible? add final version of countOrbit Aug1 revised Collatz Tool Box — any speed ups possible? replaced countOrbit with faster version Aug1 revised Collatz Tool Box — any speed ups possible? added enhanced orbit count to example Jul31 revised Collatz Tool Box — any speed ups possible? added one more function to replicate normal orbit counts Jul31 revised Collatz Tool Box — any speed ups possible? added links to conjecture info Jul31 comment Collatz Tool Box — any speed ups possible? @OleksandrR., also the $10^{477119}$ number is calculated in omegaSubOrbit[x] with x being the uniqueRank number. Both calculations are very quick--under 2 seconds. Jul31 comment Collatz Tool Box — any speed ups possible? @OleksandrR.,no, I use my short-cut, which is what this is all about. Notice these numbers from the example: $4805005, 1903828$. The first is the count of multiplies required to get down to $1$ and the second is the number of sub orbits processed to get to that number. Each sub orbit contains its own length, so the first sub orbit adds $1000000$ to the count and moves on to the next sub orbit. So, the whole thing is done with a series of additions. The key is: IntegerExponent[x+1,2] applied to the first number of the sub orbit provides that count. Jul31 comment Collatz Tool Box — any speed ups possible? @cormullion, and I had to show all the code because if you tweak one function, most likely you would have to tweak another to keep everything working together. Jul31 comment Collatz Tool Box — any speed ups possible? @cormullion, Because I'm an old procedural programmer, I feel most comfortable using For and While and I don't usually see how to eliminate them. This post is two-fold---One, to let others grab this stuff and play with it and Two, to find out how to speed up the countOrbit function to maybe get it below 10 minutes duration on my pc. Jul31 revised Collatz Tool Box — any speed ups possible? tweaked code alignment and questioned the down-votes Jul31 asked Collatz Tool Box — any speed ups possible? Jul24 awarded Fanatic Jul12 comment Building graph based on the cities connection? @rm-rf, I assumed that since he is selecting cities by population, and if he wanted one point in each state, then the resultant graph would have the most populus city of each state as the location of its vertex. I had used this approach on the travelling salesman problem 30-years ago (without any more success than the other methods.) Jul12 comment Building graph based on the cities connection? Imagine a light-house with its revolving light at each city. When the light hits another city, draw the line, unless that line crosses another. The bottom graph has no crossing lines. (i.e., it's planar.) That's the best I can do to help. Jul12 comment Building graph based on the cities connection? Bottom graph is most populus city in each state. Then there is a pruning algorithm to reduce the number of edges.